Title Page

Contents

Abstract 12

Chapter 1. Introduction 14

1.1. Background and Motivation 14

1.2. Previous research 15

1.3. Research objectives 16

Chapter 2. Cuboid-RANSAC 20

2.1. RANSAC 20

2.1.1. RANSAC Plane Fitting 21

2.2. Cuboid Reconstruction 23

2.2.1. Cuboid Reconstruction with Three Planes 24

2.2.2. Cuboid Reconstruction with Two Planes 26

2.2.3. Cuboid Reconstruction with One Plane 28

Chapter 3. Fuzzy Cuboid-RANSAC 30

3.1. Fuzzy Inference 30

3.1.1. Objective Function 31

3.1.2. Fuzzification of Data 34

3.1.3. Fuzzy Membership Functions 37

3.1.4. Fuzzy Rules 39

3.1.5. Fuzzy Inference 41

3.2. Fuzzy RANSAC 43

3.2.1. Initial Data Selection 43

3.2.2. Determining Cutoff Distance 46

3.2.3. Termination Criteria for Iteration 53

3.2.4. Fuzzy Cuboid-RANSAC Algorithm 53

Chapter 4. Experiments 58

4.1. Experimental Setup 58

4.2. Evaluation Metrics 59

4.3. Experimental Result 64

4.3.1. Surface Error 64

4.3.2. Time Duration 68

4.3.3. Box Plot for Distance 70

Chapter 5. Conclusion 74

References 76

초록 82

Table 3.1. Fuzzy rule table. 42

Table 3.2. Descriptive Statistic of point cloud. 47

Table 4.1. Root Mean Square Error 65

Table 4.2. Iteration and time duration comparison 69

Table 4.3. Distance distribution for each algorithm based on quantiles 72

Figure 2.1. The line fitting using RANSAC algorithm 22

Figure 2.2. The Example of finding third plane when only two planes exist. 27

Figure 2.3. Rotating caliper algorithms to find optimal plane 29

Figure 3.1. The relation between the normalized distance and the membership value according fuzziness m. 35

Figure 3.2. The examples of parametrized membership function 38

Figure 3.3. The fuzzy membership function of fuzzy Cuboid-RANSAC 40

Figure 3.4. The fuzzy classifier 42

Figure 3.5. The objective function graph by normalized distance 45

Figure 3.6. The distance between the point cloud assumed to follow a Gaussian distribution 47

Figure 3.7. Ensenso X36 Camera 48

Figure 3.8. The scene of plane captured by Ensenso X36 49

Figure 3.9. z-value of point cloud captured by Ensenso X36 50

Figure 3.10. QQ-plot for distributions of z-value 52

Figure 3.11. Comparisons between normalized z-value with Gaussian distribution 52

Figure 4.1. RGB image of boxes captured by Ensenso camera 60

Figure 4.2. Instance Segmentation by Sipmask model 61

Figure 4.3. Segmented point cloud for reconstructing cuboid 62

Figure 4.4. OptiTrack Equipments 63

Figure 4.5. Surface error calculation 65

Figure 4.6. Cuboid reconstruction result for actual point cloud 66

Figure 4.7. Cuboid reconstruction result for unordered scene 67

Figure 4.8. Box plot of distance between points and planes 72